library(googlesheets4) # read google sheets
library(tidyverse) # data wrangling, grammar, and manipulation
library(ggridges) # Density Plots
library(ggprism) # plots aesthetics
library(ggpubr) # plots aesthetics
library(table1) # Table 1
library(kableExtra) # Tables
library(rstatix) # Normality tests
library(lme4) # Linear Mixed Models
library(lmerTest)
library(stargazer)  #lmer and glmer mods tables
library(sjPlot) #for plotting and tableslmer and glmer mods
library(performance) # model performance and model comparison
library(flexplot)# estimates
library("sciRmdTheme") # rmarkdown theme
library(plotly)
library(irr) #ICC of JH

Overview

Biodex Data

sheet_url <- "https://docs.google.com/spreadsheets/d/1K_IxFkSIEeZF_idOxfCg7bdBrHA0q7JNbvxf0rYosvE/edit#gid=0"
biodex_data <- read_sheet(sheet_url, sheet = "Biodex Data")

jump_data <- read_sheet(sheet_url, sheet = "Jump Data")

biodex_data$Group <- factor(biodex_data$Group, levels = sort(unique(biodex_data$Group)))
biodex_data$ID <- as.factor(biodex_data$ID)

jump_data$Group <- factor(jump_data$Group, levels = sort(unique(jump_data$Group)))
jump_data$ID <- as.factor(jump_data$ID)

jump_data <- jump_data %>% mutate(JH_cm = JH * 100)
jump_data <- jump_data %>% mutate(Depth = abs(Depth))
jump_data <- jump_data %>% mutate(Depth_cm = Depth * 100)

biodex_data$Order <- 1
jump_data$Order <- 2

Df <- bind_rows(biodex_data, jump_data)

Df_long <- Df %>% select("Subject", "ID", "Age", "Height", "Weight","Bmi","BF", "Period","Group","JH","PT_E_R_B")

Distribuition plots

biodex_data %>%
  ggplot(aes(x=PTBW_E_R_B)) +
  geom_density(fill="blue", alpha=0.5) +
  ggtitle("Density of Age") +
  xlab("Peak Torque Extension (NM/BW") +
  ylab("Density") + theme_prism() + facet_grid(~Period)

biodex_data %>% group_by(Period, Group) %>% shapiro_test(PTBW_E_R_B)

## # A tibble: 18 × 5
##    Period       Group     variable   statistic     p
##    <chr>        <fct>     <chr>          <dbl> <dbl>
##  1 Baseline     trained   PTBW_E_R_B     0.914 0.384
##  2 Baseline     untrained PTBW_E_R_B     0.923 0.454
##  3 DY AG        trained   PTBW_E_R_B     0.941 0.619
##  4 DY AG        untrained PTBW_E_R_B     0.882 0.196
##  5 DY AG ANT    trained   PTBW_E_R_B     0.891 0.238
##  6 DY AG ANT    untrained PTBW_E_R_B     0.854 0.104
##  7 DY AG ST ANT trained   PTBW_E_R_B     0.908 0.341
##  8 DY AG ST ANT untrained PTBW_E_R_B     0.911 0.358
##  9 DY ANT       trained   PTBW_E_R_B     0.882 0.197
## 10 DY ANT       untrained PTBW_E_R_B     0.952 0.736
## 11 ST AG        trained   PTBW_E_R_B     0.968 0.883
## 12 ST AG        untrained PTBW_E_R_B     0.938 0.593
## 13 ST AG ANT    trained   PTBW_E_R_B     0.986 0.986
## 14 ST AG ANT    untrained PTBW_E_R_B     0.942 0.630
## 15 ST AG DY ANT trained   PTBW_E_R_B     0.975 0.933
## 16 ST AG DY ANT untrained PTBW_E_R_B     0.968 0.881
## 17 ST ANT       trained   PTBW_E_R_B     0.964 0.849
## 18 ST ANT       untrained PTBW_E_R_B     0.968 0.886

jump_data %>%
  ggplot(aes(x=JH )) +
  geom_density(fill="red", alpha=0.5) +
  ggtitle("Density of Height") +
  xlab("Jump Height (m)") +
  ylab("Density") + theme_prism()+ facet_grid(~Period)

jump_data %>% group_by(Period, Group) %>% shapiro_test(JH)

## # A tibble: 18 × 5
##    Period       Group     variable statistic      p
##    <chr>        <fct>     <chr>        <dbl>  <dbl>
##  1 Baseline     Trained   JH           0.881 0.191 
##  2 Baseline     Untrained JH           0.932 0.533 
##  3 DY AG        Trained   JH           0.939 0.600 
##  4 DY AG        Untrained JH           0.928 0.495 
##  5 DY AG ANT    Trained   JH           0.919 0.423 
##  6 DY AG ANT    Untrained JH           0.941 0.620 
##  7 DY AG ST ANT Trained   JH           0.866 0.137 
##  8 DY AG ST ANT Untrained JH           0.963 0.837 
##  9 DY ANT       Trained   JH           0.933 0.547 
## 10 DY ANT       Untrained JH           0.959 0.804 
## 11 ST AG        Trained   JH           0.913 0.375 
## 12 ST AG        Untrained JH           0.903 0.308 
## 13 ST AG ANT    Trained   JH           0.967 0.877 
## 14 ST AG ANT    Untrained JH           0.814 0.0408
## 15 ST AG DY ANT Trained   JH           0.807 0.0339
## 16 ST AG DY ANT Untrained JH           0.873 0.161 
## 17 ST ANT       Trained   JH           0.970 0.898 
## 18 ST ANT       Untrained JH           0.973 0.921

jump_data %>%
  ggplot(aes(x=RSI_mod )) +
  geom_density(fill="green", alpha=0.5) +
  ggtitle("Density of Height") +
  xlab("RSI modified") +
  ylab("Density") + theme_prism()+ facet_grid(~Period)

jump_data %>% group_by(Period, Group) %>% shapiro_test(RSI_mod)

## # A tibble: 18 × 5
##    Period       Group     variable statistic       p
##    <chr>        <fct>     <chr>        <dbl>   <dbl>
##  1 Baseline     Trained   RSI_mod      0.880 0.187  
##  2 Baseline     Untrained RSI_mod      0.919 0.425  
##  3 DY AG        Trained   RSI_mod      0.965 0.860  
##  4 DY AG        Untrained RSI_mod      0.981 0.966  
##  5 DY AG ANT    Trained   RSI_mod      0.922 0.444  
##  6 DY AG ANT    Untrained RSI_mod      0.933 0.547  
##  7 DY AG ST ANT Trained   RSI_mod      0.959 0.802  
##  8 DY AG ST ANT Untrained RSI_mod      0.938 0.592  
##  9 DY ANT       Trained   RSI_mod      0.720 0.00382
## 10 DY ANT       Untrained RSI_mod      0.853 0.103  
## 11 ST AG        Trained   RSI_mod      0.940 0.612  
## 12 ST AG        Untrained RSI_mod      0.944 0.647  
## 13 ST AG ANT    Trained   RSI_mod      0.954 0.753  
## 14 ST AG ANT    Untrained RSI_mod      0.890 0.232  
## 15 ST AG DY ANT Trained   RSI_mod      0.884 0.204  
## 16 ST AG DY ANT Untrained RSI_mod      0.896 0.268  
## 17 ST ANT       Trained   RSI_mod      0.889 0.228  
## 18 ST ANT       Untrained RSI_mod      0.906 0.324

ICC_JH <- jump_data %>% select(JH_1,JH_2,JH_3,JH_4,JH_5)
icc(ICC_JH, model = "twoway", 
  type = "consistency", unit = "average"  )

##  Average Score Intraclass Correlation
## 
##    Model: twoway 
##    Type : consistency 
## 
##    Subjects = 105 
##      Raters = 5 
##    ICC(C,5) = 0.908
## 
##  F-Test, H0: r0 = 0 ; H1: r0 > 0 
##  F(104,416) = 10.8 , p = 1.68e-71 
## 
##  95%-Confidence Interval for ICC Population Values:
##   0.877 < ICC < 0.933

Demographics

Demographics <- biodex_data %>%
  group_by(ID) %>%
  slice(1) %>%
  ungroup() %>% select(Group,Age,Height,Weight,Bmi,BF)

table1(~Age + Height + Weight + Bmi + BF | Group, data = Demographics)

	trained (N=8)	untrained (N=8)	Overall (N=16)
Age
Mean (SD)	23.8 (2.87)	25.8 (3.24)	24.8 (3.13)
Median [Min, Max]	22.5 [22.0, 30.0]	25.5 [22.0, 30.0]	23.5 [22.0, 30.0]
Height
Mean (SD)	1.73 (0.0792)	1.75 (0.0969)	1.74 (0.0861)
Median [Min, Max]	1.71 [1.64, 1.85]	1.75 [1.64, 1.87]	1.71 [1.64, 1.87]
Weight
Mean (SD)	83.6 (17.5)	87.4 (21.1)	85.5 (18.8)
Median [Min, Max]	79.7 [64.6, 117]	86.6 [61.0, 115]	82.3 [61.0, 117]
Bmi
Mean (SD)	27.7 (3.72)	28.2 (4.05)	28.0 (3.76)
Median [Min, Max]	27.7 [22.6, 34.1]	28.5 [22.5, 32.7]	28.0 [22.5, 34.1]
BF
Mean (SD)	24.3 (6.71)	26.5 (5.89)	25.4 (6.21)
Median [Min, Max]	25.5 [14.4, 33.0]	24.4 [20.4, 35.3]	24.4 [14.4, 35.3]

Biodex

PKET / BW

PKET_Group_MODEL <- lmer(PTBW_E_R_B ~ Group * Period +  (1  | ID), data = biodex_data)


summary(PKET_Group_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PTBW_E_R_B ~ Group * Period + (1 | ID)
##    Data: biodex_data
## 
## REML criterion at convergence: 1349
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.5712 -0.3890  0.0601  0.4913  3.3912 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 2492     49.92   
##  Residual             1420     37.68   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                                   Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)                        252.537     22.112  29.668  11.421 2.21e-12
## Groupuntrained                     -38.000     31.271  29.668  -1.215  0.23388
## PeriodDY AG                         30.800     18.839 112.000   1.635  0.10487
## PeriodDY AG ANT                     23.350     18.839 112.000   1.239  0.21777
## PeriodDY AG ST ANT                  34.963     18.839 112.000   1.856  0.06610
## PeriodDY ANT                        11.725     18.839 112.000   0.622  0.53495
## PeriodST AG                         -2.725     18.839 112.000  -0.145  0.88525
## PeriodST AG ANT                      8.475     18.839 112.000   0.450  0.65368
## PeriodST AG DY ANT                 -25.662     18.839 112.000  -1.362  0.17586
## PeriodST ANT                        15.400     18.839 112.000   0.817  0.41540
## Groupuntrained:PeriodDY AG          10.837     26.642 112.000   0.407  0.68495
## Groupuntrained:PeriodDY AG ANT      37.550     26.642 112.000   1.409  0.16148
## Groupuntrained:PeriodDY AG ST ANT   33.462     26.642 112.000   1.256  0.21173
## Groupuntrained:PeriodDY ANT         30.325     26.642 112.000   1.138  0.25745
## Groupuntrained:PeriodST AG          13.750     26.642 112.000   0.516  0.60680
## Groupuntrained:PeriodST AG ANT      21.487     26.642 112.000   0.807  0.42165
## Groupuntrained:PeriodST AG DY ANT   89.900     26.642 112.000   3.374  0.00102
## Groupuntrained:PeriodST ANT         35.412     26.642 112.000   1.329  0.18649
##                                      
## (Intercept)                       ***
## Groupuntrained                       
## PeriodDY AG                          
## PeriodDY AG ANT                      
## PeriodDY AG ST ANT                .  
## PeriodDY ANT                         
## PeriodST AG                          
## PeriodST AG ANT                      
## PeriodST AG DY ANT                   
## PeriodST ANT                         
## Groupuntrained:PeriodDY AG           
## Groupuntrained:PeriodDY AG ANT       
## Groupuntrained:PeriodDY AG ST ANT    
## Groupuntrained:PeriodDY ANT          
## Groupuntrained:PeriodST AG           
## Groupuntrained:PeriodST AG ANT       
## Groupuntrained:PeriodST AG DY ANT ** 
## Groupuntrained:PeriodST ANT          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Correlation matrix not shown by default, as p = 18 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

# AIC and BIC values
aic_val <- AIC(PKET_Group_MODEL)
bic_val <- BIC(PKET_Group_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 1389.026

cat("BIC:", bic_val, "\n")

## BIC: 1448.422

PKET_FULL_MODEL <- lmer(PTBW_E_R_B  ~ Period + Group  + BF  +  (1 | ID), 
                          data = biodex_data)
summary(PKET_FULL_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PTBW_E_R_B ~ Period + Group + BF + (1 | ID)
##    Data: biodex_data
## 
## REML criterion at convergence: 1420.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.1891 -0.4391  0.0783  0.5011  2.5139 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 2048     45.25   
##  Residual             1501     38.75   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                    Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)         331.092     51.967  13.840   6.371 1.83e-05 ***
## PeriodDY AG          36.219     13.699 120.000   2.644 0.009290 ** 
## PeriodDY AG ANT      42.125     13.699 120.000   3.075 0.002606 ** 
## PeriodDY AG ST ANT   51.694     13.699 120.000   3.774 0.000252 ***
## PeriodDY ANT         26.887     13.699 120.000   1.963 0.051989 .  
## PeriodST AG           4.150     13.699 120.000   0.303 0.762457    
## PeriodST AG ANT      19.219     13.699 120.000   1.403 0.163217    
## PeriodST AG DY ANT   19.288     13.699 120.000   1.408 0.161729    
## PeriodST ANT         33.106     13.699 120.000   2.417 0.017167 *  
## Groupuntrained        0.839     23.938  13.000   0.035 0.972574    
## BF                   -3.858      1.992  13.000  -1.937 0.074787 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.132                                                        
## PerdDYAGANT -0.132  0.500                                                 
## PrDYAGSTANT -0.132  0.500  0.500                                          
## PeriodDYANT -0.132  0.500  0.500  0.500                                   
## PeriodST AG -0.132  0.500  0.500  0.500  0.500                            
## PerdSTAGANT -0.132  0.500  0.500  0.500  0.500  0.500                     
## PrSTAGDYANT -0.132  0.500  0.500  0.500  0.500  0.500  0.500              
## PeriodSTANT -0.132  0.500  0.500  0.500  0.500  0.500  0.500  0.500       
## Groupuntrnd -0.051  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## BF          -0.931  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##             Grpntr
## PeriodDY AG       
## PerdDYAGANT       
## PrDYAGSTANT       
## PeriodDYANT       
## PeriodST AG       
## PerdSTAGANT       
## PrSTAGDYANT       
## PeriodSTANT       
## Groupuntrnd       
## BF          -0.184

# AIC and BIC values
aic_val <- AIC(PKET_FULL_MODEL)
bic_val <- BIC(PKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 1446.885

cat("BIC:", bic_val, "\n")

## BIC: 1485.493

tab_model(PKET_FULL_MODEL, 
          collapse.ci = TRUE,
          p.style = "numeric_stars", show.aic = TRUE, digits=3, digits.re = 3)

	PTBW E R B
Predictors	Estimates	p
(Intercept)	331.092 ^*** (228.289 – 433.895)	<0.001
Period [DY AG]	36.219 ^** (9.119 – 63.318)	0.009
Period [DY AG ANT]	42.125 ^** (15.025 – 69.225)	0.003
Period [DY AG ST ANT]	51.694 ^*** (24.594 – 78.793)	<0.001
Period [DY ANT]	26.887 (-0.212 – 53.987)	0.052
Period [ST AG]	4.150 (-22.950 – 31.250)	0.762
Period [ST AG ANT]	19.219 (-7.881 – 46.318)	0.163
Period [ST AG DY ANT]	19.287 (-7.812 – 46.387)	0.162
Period [ST ANT]	33.106 ^* (6.007 – 60.206)	0.017
Group [untrained]	0.839 (-46.516 – 48.194)	0.972
BF	-3.858 (-7.799 – 0.082)	0.055
Random Effects
σ²	1501.281
τ₀₀ _ID	2047.643
ICC	0.577
N _ID	16
Observations	144
Marginal R² / Conditional R²	0.183 / 0.655
AIC	1446.885
p<0.05 p<0.01 * p<0.001

Diagnostics

The model diagnostics seems to show that data meets all model assumptions

check_model(PKET_FULL_MODEL)

Plots

plot_model(PKET_FULL_MODEL, title = "Peak Torque Knee Extension", 
  show.intercept = TRUE, show.values = TRUE, digits = 3, value.offset = 0.2) +
  theme_prism()

Extract coefficients and Create predictions plots

In this plot the jitter dots are the observed values with the predicted values from the LMM in the geom_lines for each participant

model_coefs <- coef(PKET_FULL_MODEL)$ID %>% 
  rename(Intercept = `(Intercept)`) %>% 
  rownames_to_column("ID") %>% 
  mutate(ID = as.factor(ID))

merged_data <- left_join(biodex_data, model_coefs, by = c("ID", "BF"))

merged_data$predicted_sprint <- predict(PKET_FULL_MODEL, newdata = merged_data)

p_PTKE_ID <-  ggplot(merged_data, aes(x = Period, y = PTBW_E_R_B, group = ID, color = ID)) + 
   geom_jitter(size=0.1) + labs(x= "Stretching Type",y="Peak Torque (Nm)",
                                title="Peak Knee Extension Invidual Responses") +
   geom_line(aes(y = predicted_sprint)) + 
   theme_prism() +
   theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
   guides(color = FALSE)  # This line removes the color legend for ID

## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

p_PTKE_ID

Outlier plot

outlier <- merged_data %>% filter(ID == "6" ) %>%
  ggplot(aes(x = Period, y = PTBW_E_R_B, group = ID, color = ID)) + 
   geom_point(size=0.1) + labs(x= "Stretching Type",y="Peak Torque (Nm)",
                                title="Peak Knee Extension Outlier Responses") +
   geom_line() + 
   theme_prism() +
   theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
   guides(color = FALSE)  # This line removes the color legend for ID
ggplotly(outlier)

Plot model estimates

# Predict overall estimates without considering the random effects
overall_predictions <- predict(PKET_FULL_MODEL, newdata = biodex_data, re.form = NA)
biodex_data$overall_predictions <- overall_predictions


# Aggregate the predictions
biodex_data_agg <- biodex_data %>%
  group_by(Period) %>%
  summarise(mean_prediction = mean(overall_predictions, na.rm = TRUE))

p_PTKE_box <- biodex_data %>% 
  ggboxplot(x="Period", y="PTBW_E_R_B",color="Period", add="jitter",
  xlab = "Stretching Type", ylab = "Peak Torque (Nm)", title = "Peak Knee Extension")  + 
  geom_point(data=biodex_data_agg, aes(y=mean_prediction), color="red", size=3) + # Adding the aggregated model's estimates
  geom_line(data=biodex_data_agg, aes(y=mean_prediction, group=1), color="red", size=1) +
  theme_prism() +
  guides(color = FALSE)+
   theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))
p_PTKE_box

PAvg pt

avgKET_FULL_MODEL <- lmer(Av_PT_E_R_B  ~ Period + Group  + BF  +  (1 | ID), 
                          data = biodex_data)
summary(avgKET_FULL_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Av_PT_E_R_B ~ Period + Group + BF + (1 | ID)
##    Data: biodex_data
## 
## REML criterion at convergence: 1381.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.8702 -0.5086  0.0797  0.5629  2.1822 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept)  772.8   27.80   
##  Residual             1191.2   34.51   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                    Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)         122.691     33.703  14.652   3.640  0.00250 ** 
## PeriodDY AG          20.888     12.202 120.000   1.712  0.08953 .  
## PeriodDY AG ANT      37.706     12.202 120.000   3.090  0.00249 ** 
## PeriodDY AG ST ANT   50.294     12.202 120.000   4.122 6.96e-05 ***
## PeriodDY ANT         23.550     12.202 120.000   1.930  0.05597 .  
## PeriodST AG          13.200     12.202 120.000   1.082  0.28153    
## PeriodST AG ANT      20.681     12.202 120.000   1.695  0.09270 .  
## PeriodST AG DY ANT    9.431     12.202 120.000   0.773  0.44110    
## PeriodST ANT         28.838     12.202 120.000   2.363  0.01972 *  
## Groupuntrained       -1.822     15.304  13.000  -0.119  0.90707    
## BF                    1.801      1.273  13.000   1.415  0.18069    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.181                                                        
## PerdDYAGANT -0.181  0.500                                                 
## PrDYAGSTANT -0.181  0.500  0.500                                          
## PeriodDYANT -0.181  0.500  0.500  0.500                                   
## PeriodST AG -0.181  0.500  0.500  0.500  0.500                            
## PerdSTAGANT -0.181  0.500  0.500  0.500  0.500  0.500                     
## PrSTAGDYANT -0.181  0.500  0.500  0.500  0.500  0.500  0.500              
## PeriodSTANT -0.181  0.500  0.500  0.500  0.500  0.500  0.500  0.500       
## Groupuntrnd -0.050  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## BF          -0.918  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##             Grpntr
## PeriodDY AG       
## PerdDYAGANT       
## PrDYAGSTANT       
## PeriodDYANT       
## PeriodST AG       
## PerdSTAGANT       
## PrSTAGDYANT       
## PeriodSTANT       
## Groupuntrnd       
## BF          -0.184

# AIC and BIC values
aic_val <- AIC(avgKET_FULL_MODEL)
bic_val <- BIC(avgKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 1407.49

cat("BIC:", bic_val, "\n")

## BIC: 1446.097

avgpowerKET_FULL_MODEL <- lmer(Av_Power_E_R_B  ~ Period + Group  + BF  +  (1 | ID), 
                          data = biodex_data)
summary(avgpowerKET_FULL_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Av_Power_E_R_B ~ Period + Group + BF + (1 | ID)
##    Data: biodex_data
## 
## REML criterion at convergence: 1428.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2904 -0.4077  0.0631  0.4063  8.1223 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept)  154.3   12.42   
##  Residual             1937.3   44.01   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)        102.6406    23.3325  20.0641   4.399 0.000275 ***
## PeriodDY AG         20.0000    15.5615 120.0000   1.285 0.201191    
## PeriodDY AG ANT     33.5687    15.5615 120.0000   2.157 0.032987 *  
## PeriodDY AG ST ANT  40.3125    15.5615 120.0000   2.591 0.010770 *  
## PeriodDY ANT        20.9687    15.5615 120.0000   1.347 0.180367    
## PeriodST AG          9.3375    15.5615 120.0000   0.600 0.549613    
## PeriodST AG ANT     10.6250    15.5615 120.0000   0.683 0.496066    
## PeriodST AG DY ANT  32.2125    15.5615 120.0000   2.070 0.040597 *  
## PeriodST ANT        25.7250    15.5615 120.0000   1.653 0.100922    
## Groupuntrained       8.7443     9.7792  13.0000   0.894 0.387484    
## BF                   0.5311     0.8137  13.0000   0.653 0.525316    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.333                                                        
## PerdDYAGANT -0.333  0.500                                                 
## PrDYAGSTANT -0.333  0.500  0.500                                          
## PeriodDYANT -0.333  0.500  0.500  0.500                                   
## PeriodST AG -0.333  0.500  0.500  0.500  0.500                            
## PerdSTAGANT -0.333  0.500  0.500  0.500  0.500  0.500                     
## PrSTAGDYANT -0.333  0.500  0.500  0.500  0.500  0.500  0.500              
## PeriodSTANT -0.333  0.500  0.500  0.500  0.500  0.500  0.500  0.500       
## Groupuntrnd -0.047  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## BF          -0.847  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##             Grpntr
## PeriodDY AG       
## PerdDYAGANT       
## PrDYAGSTANT       
## PeriodDYANT       
## PeriodST AG       
## PerdSTAGANT       
## PrSTAGDYANT       
## PeriodSTANT       
## Groupuntrnd       
## BF          -0.184

# AIC and BIC values
aic_val <- AIC(avgpowerKET_FULL_MODEL)
bic_val <- BIC(avgpowerKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 1454.206

cat("BIC:", bic_val, "\n")

## BIC: 1492.814

ratioKET_FULL_MODEL <- lmer(AGANT_Ratio_R_B  ~ Period + Group  + BF  +  (1 | ID), 
                          data = biodex_data)
summary(ratioKET_FULL_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: AGANT_Ratio_R_B ~ Period + Group + BF + (1 | ID)
##    Data: biodex_data
## 
## REML criterion at convergence: 1040.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8662 -0.4459  0.0015  0.4309  3.8471 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 62.44    7.902   
##  Residual             91.49    9.565   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                     Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)         46.47661    9.53353  14.58015   4.875 0.000219 ***
## PeriodDY AG         -0.94750    3.38169 120.00000  -0.280 0.779818    
## PeriodDY AG ANT      1.48000    3.38169 120.00000   0.438 0.662426    
## PeriodDY AG ST ANT  -0.49687    3.38169 120.00000  -0.147 0.883433    
## PeriodDY ANT         0.97563    3.38169 120.00000   0.289 0.773460    
## PeriodST AG          2.54688    3.38169 120.00000   0.753 0.452843    
## PeriodST AG ANT     -1.11375    3.38169 120.00000  -0.329 0.742468    
## PeriodST AG DY ANT   2.15375    3.38169 120.00000   0.637 0.525413    
## PeriodST ANT         5.71750    3.38169 120.00000   1.691 0.093486 .  
## Groupuntrained       2.19376    4.33444  13.00000   0.506 0.621244    
## BF                  -0.03528    0.36066  13.00000  -0.098 0.923559    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.177                                                        
## PerdDYAGANT -0.177  0.500                                                 
## PrDYAGSTANT -0.177  0.500  0.500                                          
## PeriodDYANT -0.177  0.500  0.500  0.500                                   
## PeriodST AG -0.177  0.500  0.500  0.500  0.500                            
## PerdSTAGANT -0.177  0.500  0.500  0.500  0.500  0.500                     
## PrSTAGDYANT -0.177  0.500  0.500  0.500  0.500  0.500  0.500              
## PeriodSTANT -0.177  0.500  0.500  0.500  0.500  0.500  0.500  0.500       
## Groupuntrnd -0.050  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## BF          -0.919  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##             Grpntr
## PeriodDY AG       
## PerdDYAGANT       
## PrDYAGSTANT       
## PeriodDYANT       
## PeriodST AG       
## PerdSTAGANT       
## PrSTAGDYANT       
## PeriodSTANT       
## Groupuntrnd       
## BF          -0.184

# AIC and BIC values
aic_val <- AIC(ratioKET_FULL_MODEL)
bic_val <- BIC(ratioKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 1066.709

cat("BIC:", bic_val, "\n")

## BIC: 1105.316

Vertical Jump Data

JH_Group_MODEL <- lmer(JH_cm ~ Group * Period +  (1  | ID), data = jump_data)


summary(JH_Group_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: JH_cm ~ Group * Period + (1 | ID)
##    Data: jump_data
## 
## REML criterion at convergence: 706.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3704 -0.4794 -0.0185  0.4741  3.8970 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 8.872    2.979   
##  Residual             9.199    3.033   
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                                     Estimate Std. Error         df t value
## (Intercept)                        3.413e+01  1.503e+00  4.303e+01  22.705
## GroupUntrained                    -8.250e+00  2.126e+00  4.303e+01  -3.881
## PeriodDY AG                        1.250e-01  1.517e+00  1.120e+02   0.082
## PeriodDY AG ANT                    7.500e-01  1.517e+00  1.120e+02   0.495
## PeriodDY AG ST ANT                 2.250e+00  1.517e+00  1.120e+02   1.484
## PeriodDY ANT                      -1.975e-13  1.517e+00  1.120e+02   0.000
## PeriodST AG                       -1.250e-01  1.517e+00  1.120e+02  -0.082
## PeriodST AG ANT                   -2.500e-01  1.517e+00  1.120e+02  -0.165
## PeriodST AG DY ANT                 1.250e-01  1.517e+00  1.120e+02   0.082
## PeriodST ANT                       1.500e+00  1.517e+00  1.120e+02   0.989
## GroupUntrained:PeriodDY AG         1.875e+00  2.145e+00  1.120e+02   0.874
## GroupUntrained:PeriodDY AG ANT     3.000e+00  2.145e+00  1.120e+02   1.399
## GroupUntrained:PeriodDY AG ST ANT  6.250e-01  2.145e+00  1.120e+02   0.291
## GroupUntrained:PeriodDY ANT        2.000e+00  2.145e+00  1.120e+02   0.933
## GroupUntrained:PeriodST AG         1.000e+00  2.145e+00  1.120e+02   0.466
## GroupUntrained:PeriodST AG ANT     2.125e+00  2.145e+00  1.120e+02   0.991
## GroupUntrained:PeriodST AG DY ANT  1.625e+00  2.145e+00  1.120e+02   0.758
## GroupUntrained:PeriodST ANT        1.000e+00  2.145e+00  1.120e+02   0.466
##                                   Pr(>|t|)    
## (Intercept)                        < 2e-16 ***
## GroupUntrained                    0.000352 ***
## PeriodDY AG                       0.934456    
## PeriodDY AG ANT                   0.621886    
## PeriodDY AG ST ANT                0.140709    
## PeriodDY ANT                      1.000000    
## PeriodST AG                       0.934456    
## PeriodST AG ANT                   0.869359    
## PeriodST AG DY ANT                0.934456    
## PeriodST ANT                      0.324745    
## GroupUntrained:PeriodDY AG        0.383852    
## GroupUntrained:PeriodDY AG ANT    0.164635    
## GroupUntrained:PeriodDY AG ST ANT 0.771271    
## GroupUntrained:PeriodDY ANT       0.353066    
## GroupUntrained:PeriodST AG        0.641930    
## GroupUntrained:PeriodST AG ANT    0.323910    
## GroupUntrained:PeriodST AG DY ANT 0.450231    
## GroupUntrained:PeriodST ANT       0.641930    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Correlation matrix not shown by default, as p = 18 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

# AIC and BIC values
aic_val <- AIC(JH_Group_MODEL)
bic_val <- BIC(JH_Group_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 746.3944

cat("BIC:", bic_val, "\n")

## BIC: 805.7907

JH_OPT_MODEL <- lmer(JH_cm ~  Period + BF + Weight  + (1  + Depth_cm| ID), data = jump_data)


summary(JH_OPT_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: JH_cm ~ Period + BF + Weight + (1 + Depth_cm | ID)
##    Data: jump_data
## 
## REML criterion at convergence: 734.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0600 -0.4814 -0.0121  0.4912  3.7058 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 161.6899 12.7157       
##           Depth_cm      0.2635  0.5133  -0.99
##  Residual               7.3301  2.7074       
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                     Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)         29.82276    3.37544   6.72742   8.835 6.08e-05 ***
## PeriodDY AG          1.01561    0.97105 111.89782   1.046   0.2979    
## PeriodDY AG ANT      2.03852    0.98993 111.47666   2.059   0.0418 *  
## PeriodDY AG ST ANT   1.57739    1.00723 113.52988   1.566   0.1201    
## PeriodDY ANT         0.64131    0.97645 114.60066   0.657   0.5126    
## PeriodST AG          0.33493    0.97605 113.85160   0.343   0.7321    
## PeriodST AG ANT      0.40290    0.97049 112.70082   0.415   0.6788    
## PeriodST AG DY ANT   0.44793    0.97613 113.62907   0.459   0.6472    
## PeriodST ANT         2.02325    0.98382 115.69261   2.057   0.0420 *  
## BF                  -0.30885    0.17897   9.67892  -1.726   0.1161    
## Weight               0.08598    0.05963   9.28322   1.442   0.1822    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.145                                                        
## PerdDYAGANT -0.175  0.507                                                 
## PrDYAGSTANT -0.179  0.502  0.529                                          
## PeriodDYANT -0.141  0.507  0.509  0.510                                   
## PeriodST AG -0.126  0.510  0.507  0.503  0.514                            
## PerdSTAGANT -0.116  0.499  0.508  0.504  0.499  0.497                     
## PrSTAGDYANT -0.137  0.502  0.499  0.496  0.503  0.508  0.496              
## PeriodSTANT -0.133  0.504  0.507  0.501  0.513  0.512  0.496  0.507       
## BF          -0.199 -0.004 -0.049 -0.072  0.004  0.015 -0.074 -0.037 -0.024
## Weight      -0.451  0.012  0.078  0.104  0.002 -0.018  0.056  0.034  0.022
##             BF    
## PeriodDY AG       
## PerdDYAGANT       
## PrDYAGSTANT       
## PeriodDYANT       
## PeriodST AG       
## PerdSTAGANT       
## PrSTAGDYANT       
## PeriodSTANT       
## BF                
## Weight      -0.767

# AIC and BIC values
aic_val <- AIC(JH_OPT_MODEL)
bic_val <- BIC(JH_OPT_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 764.1869

cat("BIC:", bic_val, "\n")

## BIC: 808.7341

Diagnostics

The model diagnostics seems to show that data meets all model assumptions

check_model(JH_OPT_MODEL)

Plots

plot_model(JH_OPT_MODEL, title = "Vertical Jump Height", 
  show.intercept = TRUE, show.values = TRUE, digits = 3, value.offset = 0.2) +
  theme_prism()

Extract coefficients and Create predictions plots

In this plot the jitter dots are the observed values with the predicted values from the LMM in the geom_lines for each participant

model_coefs <- coef(JH_OPT_MODEL)$ID %>% 
  rename(Intercept = `(Intercept)`) %>% 
  rownames_to_column("ID") %>% 
  mutate(ID = as.factor(ID))

merged_data <- left_join(jump_data, model_coefs, by = c("ID", "Weight", "BF", "Depth_cm"))

merged_data$predicted_jump <- predict(JH_OPT_MODEL, newdata = merged_data)

p_JH_ID <-  ggplot(merged_data, aes(x = Period, y = JH_cm, group = ID, color = ID)) + 
   geom_jitter(size=0.1) + labs(x= "Stretching Type",y="Height (cm)",
                               title= "Jump Height Individual Responses") +
   geom_line(aes(y = predicted_jump)) + 
   theme_prism() +
   theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
   guides(color = FALSE)  # This line removes the color legend for ID
p_JH_ID

Plot model estimates

# Predict overall estimates without considering the random effects
overall_predictions <- predict(JH_OPT_MODEL, newdata = jump_data, re.form = NA)
jump_data$overall_predictions <- overall_predictions


# Aggregate the predictions
jump_data_agg <- jump_data %>%
  group_by(Period) %>%
  summarise(mean_prediction = mean(overall_predictions, na.rm = TRUE))

jump_data$Group <- factor(jump_data$Group, levels = sort(unique(jump_data$Group)))


p_JH_box <- jump_data %>% 
  ggboxplot(x="Period", y="JH_cm",color="Period", add="jitter",
  xlab = "Stretching Type", ylab = "Height (cm)", title = "Vertical Jump Height")  + 
  geom_point(data=jump_data_agg, aes(y=mean_prediction), color="red", size=3) + # Adding the aggregated model's estimates
  geom_line(data=jump_data_agg, aes(y=mean_prediction, group=1), color="red", size=1) +
  theme_prism() +
  guides(color = FALSE)+
   theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))
p_JH_box

ggarrange(p_PTKE_box,p_PTKE_ID,p_JH_box,p_JH_ID)

ggsave("Torque_JH.png")

## Saving 11 x 10 in image

RSImod_OPT_MODEL <- lmer(RSI_mod ~ Group + Period + BF + Weight +Depth_cm + (1 + Depth_cm | ID), data = jump_data)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues

## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e+00

summary(RSImod_OPT_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RSI_mod ~ Group + Period + BF + Weight + Depth_cm + (1 + Depth_cm |  
##     ID)
##    Data: jump_data
## 
## REML criterion at convergence: 142.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1299 -0.4976 -0.1045  0.3414  5.0312 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  ID       (Intercept) 1.573e-05 0.003966      
##           Depth_cm    1.659e-04 0.012881 -0.63
##  Residual             8.956e-02 0.299262      
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                      Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)          0.468857   0.454506   9.844051   1.032 0.326949    
## GroupUntrained       0.433052   0.179238   7.065416   2.416 0.046041 *  
## PeriodDY AG         -0.125452   0.106193 118.407166  -1.181 0.239829    
## PeriodDY AG ANT     -0.301816   0.106947 119.870936  -2.822 0.005587 ** 
## PeriodDY AG ST ANT  -0.248867   0.109480 121.539996  -2.273 0.024771 *  
## PeriodDY ANT        -0.086719   0.106602 119.173309  -0.813 0.417562    
## PeriodST AG         -0.118174   0.106214 118.382603  -1.113 0.268133    
## PeriodST AG ANT     -0.124406   0.105910 117.774239  -1.175 0.242509    
## PeriodST AG DY ANT  -0.015773   0.107096 119.759983  -0.147 0.883159    
## PeriodST ANT        -0.226123   0.106209 118.252485  -2.129 0.035326 *  
## BF                   0.002982   0.020034   6.616414   0.149 0.886094    
## Weight               0.003761   0.006517   5.308064   0.577 0.587474    
## Depth_cm             0.033989   0.009065  45.336062   3.749 0.000501 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

# AIC and BIC values
aic_val <- AIC(RSImod_OPT_MODEL)
bic_val <- BIC(RSImod_OPT_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: 176.5005

cat("BIC:", bic_val, "\n")

## BIC: 226.9873

Impulse_OPT_MODEL <- lmer(Relative_net_impulse ~  Period + BF + Weight + Depth_cm + (1  + Depth_cm| ID), data = jump_data)

## boundary (singular) fit: see help('isSingular')

summary(Impulse_OPT_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Relative_net_impulse ~ Period + BF + Weight + Depth_cm + (1 +  
##     Depth_cm | ID)
##    Data: jump_data
## 
## REML criterion at convergence: -61.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8001 -0.5075 -0.1722  0.2720  5.9999 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  ID       (Intercept) 1.962e-02 0.140089      
##           Depth_cm    5.741e-05 0.007577 -1.00
##  Residual             2.154e-02 0.146782      
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                      Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)          0.376408   0.116639  30.735494   3.227 0.002967 ** 
## PeriodDY AG          0.003520   0.052030 120.370145   0.068 0.946174    
## PeriodDY AG ANT     -0.034345   0.052205 120.562994  -0.658 0.511869    
## PeriodDY AG ST ANT  -0.022749   0.052654 121.338816  -0.432 0.666474    
## PeriodDY ANT         0.053374   0.052108 120.827567   1.024 0.307736    
## PeriodST AG         -0.026650   0.052067 120.876215  -0.512 0.609698    
## PeriodST AG ANT      0.005221   0.051984 120.429834   0.100 0.920168    
## PeriodST AG DY ANT  -0.005941   0.052183 120.938262  -0.114 0.909541    
## PeriodST ANT        -0.046175   0.052070 120.669813  -0.887 0.376958    
## BF                   0.002933   0.004618  46.496772   0.635 0.528518    
## Weight               0.003784   0.001553  80.434488   2.437 0.017024 *  
## Depth_cm             0.012098   0.002959  18.419307   4.088 0.000662 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.212                                                        
## PerdDYAGANT -0.213  0.502                                                 
## PrDYAGSTANT -0.186  0.499  0.505                                          
## PeriodDYANT -0.199  0.502  0.502  0.502                                   
## PeriodST AG -0.205  0.502  0.501  0.498  0.503                            
## PerdSTAGANT -0.203  0.500  0.500  0.497  0.499  0.499                     
## PrSTAGDYANT -0.207  0.500  0.499  0.497  0.500  0.501  0.497              
## PeriodSTANT -0.210  0.501  0.501  0.496  0.501  0.502  0.499  0.501       
## BF          -0.423 -0.018 -0.023 -0.035 -0.021 -0.020 -0.027 -0.036 -0.028
## Weight      -0.285  0.026  0.049  0.066  0.024  0.017  0.013  0.046  0.028
## Depth_cm    -0.296 -0.028 -0.058 -0.107 -0.042 -0.023 -0.007 -0.049 -0.022
##             BF     Weight
## PeriodDY AG              
## PerdDYAGANT              
## PrDYAGSTANT              
## PeriodDYANT              
## PeriodST AG              
## PerdSTAGANT              
## PrSTAGDYANT              
## PeriodSTANT              
## BF                       
## Weight      -0.586       
## Depth_cm     0.122 -0.366
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

# AIC and BIC values
aic_val <- AIC(Impulse_OPT_MODEL)
bic_val <- BIC(Impulse_OPT_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: -29.30643

cat("BIC:", bic_val, "\n")

## BIC: 18.21058

PF_OPT_MODEL <- lmer(Jump_time ~  Period + BF + Weight + Depth_cm + (1  + Depth_cm| ID), data = jump_data)

## boundary (singular) fit: see help('isSingular')

summary(PF_OPT_MODEL)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Jump_time ~ Period + BF + Weight + Depth_cm + (1 + Depth_cm |      ID)
##    Data: jump_data
## 
## REML criterion at convergence: -215.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.2556 -0.6041 -0.2001  0.2627  4.7141 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  ID       (Intercept) 2.439e-03 0.049385      
##           Depth_cm    4.901e-06 0.002214 -1.00
##  Residual             7.337e-03 0.085656      
## Number of obs: 144, groups:  ID, 16
## 
## Fixed effects:
##                      Estimate Std. Error         df t value Pr(>|t|)  
## (Intercept)         8.338e-02  5.013e-02  3.736e+01   1.663   0.1046  
## PeriodDY AG         5.000e-03  3.034e-02  1.243e+02   0.165   0.8694  
## PeriodDY AG ANT    -3.276e-02  3.044e-02  1.249e+02  -1.076   0.2839  
## PeriodDY AG ST ANT -1.667e-02  3.065e-02  1.253e+02  -0.544   0.5875  
## PeriodDY ANT        1.184e-02  3.036e-02  1.244e+02   0.390   0.6972  
## PeriodST AG        -8.176e-03  3.034e-02  1.245e+02  -0.269   0.7880  
## PeriodST AG ANT     1.190e-02  3.032e-02  1.243e+02   0.393   0.6953  
## PeriodST AG DY ANT -1.286e-02  3.038e-02  1.245e+02  -0.423   0.6729  
## PeriodST ANT       -2.182e-02  3.035e-02  1.247e+02  -0.719   0.4736  
## BF                  3.926e-03  2.069e-03  3.579e+01   1.898   0.0659 .
## Weight              3.961e-04  7.557e-04  3.592e+01   0.524   0.6034  
## Depth_cm           -5.797e-05  1.281e-03  1.379e+01  -0.045   0.9645  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.288                                                        
## PerdDYAGANT -0.279  0.502                                                 
## PrDYAGSTANT -0.258  0.500  0.506                                          
## PeriodDYANT -0.283  0.502  0.502  0.502                                   
## PeriodST AG -0.287  0.501  0.501  0.500  0.502                            
## PerdSTAGANT -0.289  0.500  0.501  0.499  0.500  0.500                     
## PrSTAGDYANT -0.281  0.501  0.501  0.501  0.501  0.501  0.500              
## PeriodSTANT -0.291  0.501  0.501  0.499  0.501  0.501  0.500  0.501       
## BF          -0.305 -0.014 -0.030 -0.049 -0.016 -0.011 -0.020 -0.024 -0.015
## Weight      -0.197  0.021  0.047  0.077  0.026  0.015  0.018  0.033  0.022
## Depth_cm    -0.368 -0.036 -0.070 -0.125 -0.048 -0.031 -0.021 -0.055 -0.031
##             BF     Weight
## PeriodDY AG              
## PerdDYAGANT              
## PrDYAGSTANT              
## PeriodDYANT              
## PeriodST AG              
## PerdSTAGANT              
## PrSTAGDYANT              
## PeriodSTANT              
## BF                       
## Weight      -0.726       
## Depth_cm     0.270 -0.461
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

# AIC and BIC values
aic_val <- AIC(PF_OPT_MODEL)
bic_val <- BIC(PF_OPT_MODEL)
cat("AIC:", aic_val, "\n")

## AIC: -183.927

cat("BIC:", bic_val, "\n")

## BIC: -136.41

tab_model(PKET_FULL_MODEL,avgKET_FULL_MODEL,avgpowerKET_FULL_MODEL,
          dv.labels = c("Peak Torque Knee Extension (N-m/bw)", "Average Torque Knee Extension (N-m)",
                        "Average Power Knee Extension (Watts)"),
          show.reflvl = T, show.intercept = T, p.style = "numeric_stars", collapse.ci = TRUE)

	Peak Torque Knee Extension (N-m/bw)		Average Torque Knee Extension (N-m)		Average Power Knee Extension (Watts)
Predictors	Estimates	p	Estimates	p	Estimates	p
(Intercept)	331.09 ^*** (228.29 – 433.89)	<0.001	122.69 ^*** (56.02 – 189.36)	<0.001	102.64 ^*** (56.48 – 148.80)	<0.001
BF	-3.86 (-7.80 – 0.08)	0.055	1.80 (-0.72 – 4.32)	0.160	0.53 (-1.08 – 2.14)	0.515
trained	Reference		Reference		Reference
untrained	0.84 (-46.52 – 48.19)	0.972	-1.82 (-32.10 – 28.45)	0.905	8.74 (-10.60 – 28.09)	0.373
PeriodDY AG	36.22 ^** (9.12 – 63.32)	0.009	20.89 (-3.25 – 45.03)	0.089	20.00 (-10.78 – 50.78)	0.201
PeriodDY AG ANT	42.12 ^** (15.03 – 69.22)	0.003	37.71 ^** (13.57 – 61.85)	0.002	33.57 ^* (2.78 – 64.35)	0.033
PeriodDY AG ST ANT	51.69 ^*** (24.59 – 78.79)	<0.001	50.29 ^*** (26.15 – 74.43)	<0.001	40.31 ^* (9.53 – 71.10)	0.011
PeriodDY ANT	26.89 (-0.21 – 53.99)	0.052	23.55 (-0.59 – 47.69)	0.056	20.97 (-9.82 – 51.75)	0.180
PeriodST AG	4.15 (-22.95 – 31.25)	0.762	13.20 (-10.94 – 37.34)	0.281	9.34 (-21.45 – 40.12)	0.550
PeriodST AG ANT	19.22 (-7.88 – 46.32)	0.163	20.68 (-3.46 – 44.82)	0.092	10.62 (-20.16 – 41.41)	0.496
PeriodST AG DY ANT	19.29 (-7.81 – 46.39)	0.162	9.43 (-14.71 – 33.57)	0.441	32.21 ^* (1.43 – 63.00)	0.040
PeriodST ANT	33.11 ^* (6.01 – 60.21)	0.017	28.84 ^* (4.70 – 52.98)	0.020	25.72 (-5.06 – 56.51)	0.101
Random Effects
σ²	1501.28		1191.19		1937.29
τ₀₀	2047.64 _ID		772.78 _ID		154.31 _ID
ICC	0.58		0.39		0.07
N	16 _ID		16 _ID		16 _ID
Observations	144		144		144
Marginal R² / Conditional R²	0.183 / 0.655		0.139 / 0.478		0.082 / 0.150
p<0.05 p<0.01 * p<0.001

tab_model(JH_OPT_MODEL,Impulse_OPT_MODEL,  
          dv.labels = c("Jump Height (cm)", "Relative Net Impulse (N-s/bw)"),
          show.reflvl = T, show.intercept = T, p.style = "numeric_stars", collapse.ci = TRUE)

	Jump Height (cm)		Relative Net Impulse (N-s/bw)
Predictors	Estimates	p	Estimates	p
(Intercept)	29.82 ^*** (23.14 – 36.50)	<0.001	0.38 ^** (0.15 – 0.61)	0.002
BF	-0.31 (-0.66 – 0.05)	0.087	0.00 (-0.01 – 0.01)	0.527
Depth_cm			0.01 ^*** (0.01 – 0.02)	<0.001
PeriodDY AG	1.02 (-0.91 – 2.94)	0.298	0.00 (-0.10 – 0.11)	0.946
PeriodDY AG ANT	2.04 ^* (0.08 – 4.00)	0.041	-0.03 (-0.14 – 0.07)	0.512
PeriodDY AG ST ANT	1.58 (-0.42 – 3.57)	0.120	-0.02 (-0.13 – 0.08)	0.666
PeriodDY ANT	0.64 (-1.29 – 2.57)	0.512	0.05 (-0.05 – 0.16)	0.308
PeriodST AG	0.33 (-1.60 – 2.27)	0.732	-0.03 (-0.13 – 0.08)	0.610
PeriodST AG ANT	0.40 (-1.52 – 2.32)	0.679	0.01 (-0.10 – 0.11)	0.920
PeriodST AG DY ANT	0.45 (-1.48 – 2.38)	0.647	-0.01 (-0.11 – 0.10)	0.910
PeriodST ANT	2.02 ^* (0.08 – 3.97)	0.042	-0.05 (-0.15 – 0.06)	0.377
Weight	0.09 (-0.03 – 0.20)	0.152	0.00 ^* (0.00 – 0.01)	0.016
Random Effects
σ²	7.33		0.02
τ₀₀	161.69 _ID		0.02 _ID
τ₁₁	0.26 _{ID.Depth_cm}		0.00 _{ID.Depth_cm}
ρ₀₁	-0.99 _ID		-1.00 _ID
ICC	0.96		0.32
N	16 _ID		16 _ID
Observations	144		144
Marginal R² / Conditional R²	0.014 / 0.957		0.429 / 0.613
p<0.05 p<0.01 * p<0.001

Effects Of Diff ects Of Different Str ent Stretching Modalities On The Antagonist And etching Modalities On The Antagonist And Agonist Muscles On Isokinetic Strength And Vertical Jump Performance

Samuel Montalvo, Ph.D.

2023-10-21

Overview

Biodex Data

Distribuition plots

Demographics

Biodex

PKET / BW

Diagnostics

Plots

Outlier plot

PAvg pt

Vertical Jump Data

Diagnostics

Plots